The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
DOI:
https://doi.org/10.15407/mag14.01.016Ключові слова:
дискретне рiвняння синус-Ґордона, нелiнiйнi осцилятори, двовимiрна ґратка, гетероклiнiчнi рухомi хвилi, критичнi точки, принцип концентрованої компактностiАнотація
Статтю присвячено дискретному рiвнянню синус-Ґордона, яке описує нескiнченну систему нелiнiйно зв’язаних нелiнiйних осциляторiв на двовимiрнiй ґратцi iз зовнiшнiм потенцiалом V (r) = K(1 - cos r). Основний результат стосується iснування розв’язкiв у виглядi гетероклiнiчних рухомих хвиль. За допомогою методу критичних точок i принципу концентрованої компактностi отримано достатнi умови iснування таких розв’язкiв.
Mathematical Subject Classification: 34G20, 37K60, 58E50.
Посилання
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